There are growing calls for a public inquiry into UK involvement in torture following last week's publication of the Senate report. Photograph: Saul Loeb/AFP/Getty Images

The parliamentary inquiry into the involvement of British intelligence agents in the torture of terror suspects is not afraid to embarrass the prime minister and former senior political figures, its head, Sir Malcolm Rifkind, has said.

Rifkind, the chairman of parliament’s intelligence and security committee (ISC), promised he would investigate “without fear or favour” and would request secret material relating to the UK that was redacted from a damning US report about torture by the CIA.

The Conservative MP said he would not be able to see all of the censored material but the committee would ask to examine anything taken out of the report at the request of the UK agencies.

Rifkind, a former foreign secretary, promised to conduct a thorough investigation amid claims that his group of MPs and peers is not independent enough to get to the bottom of the scandal.

There are growing calls for a public inquiry into UK involvement in torture in the wake of 9/11, after the US Senate report into the mistreatment of detainees found the CIA used brutal and ineffective methods. Yvette Cooper, the shadow home secretary, joined those voices on Sunday, saying it was her instinct that a judge-led inquiry was the right thing to do.

However, Rifkind said he would not shy away from revealing details that were embarrassing for the security services or for the government.

He told the BBC’s Andrew Marr Show he would not be able to see all of the redacted material but the committee would ask to examine anything taken out of the report at the request of the UK agencies.

“We are going to request the Americans – we cannot instruct the United States government – but we are going to request them, not to see the whole redacted stuff because a lot of it’s got nothing to do with the United Kingdom, but any references there may be to the United Kingdom and the United Kingdom’s possible involvement in these matters. If that was redacted in the public report, yes, we want to see that.

“In the United Kingdom, anything can only be redacted on national security grounds. And if the prime minister tried to redact one of our reports simply to prevent political embarrassment, we would make a huge public fuss about it. Now we hope the same principle applies in America. That’s what we have to test.”

Downing Street initially said there had been no requests for redactions but later admitted the UK intelligence agencies were granted deletions from the executive summary on the grounds of national security.

There are concerns that the ISC investigation will not be sufficiently independent because it is largely composed of former establishment figures, its meetings are mainly conducted in secret, and its reports are subject to redactions by the government. It also will not compel witnesses to give evidence and those who do are not speaking under oath.

However, Rifkind insisted the committee would publish a report “without fear or favour” and said it was worrying that a former Home Office minister, Lord West had suggested British agents could have been in the same building at the time US operatives were torturing suspects.

“If Lord West, what is attributed to him, is correct, if British intelligence officials were present when people were being tortured, then they were complicit in that torture. That would be quite against all the standards of this country,” he said.

“It would be something that ought to be brought into the public domain. So we have to obviously have the evidence to support that. But if that is what Lord West is saying, he was a security minister in the government at the time, so clearly he will be someone whose views we will wish to cross-examine very carefully.”

Asked whether specific former ministers including Tony Blair and David Miliband would be asked to give evidence, Rifkind said he could not yet confirm who would be asked to appear as a witness.

Rifkind’s committee took on the job of investigating the torture of detainees after Sir Peter Gibson, a retired judge, was frustrated in his inquiry because two police investigations had been launched into the rendition of detainees to Libya.

In an interim report, Gibson had not found any evidence of British agents themselves undertaking torture but he raised 27 serious questions that had not been answered about their potential involvement in what the CIA was doing. This includes whether the two intelligence agencies were willing to “condone, encourage or take advantage of rendition operations” mounted by others.

Dominic Grieve, the Conservative former attorney general, has backed the idea of allowing Gibson to resume his inquiry following the publication of the ISC report and a decision by the police about prosecution.

However, the government has appeared lukewarm so far about the revival of the Gibson inquiry, saying it will wait and see what the ISC comes up with before ordering another investigation.

David Cameron, the prime minister, has insisted that the UK has dealt with the problem of British complicity in torture and the problems date back more than a decade to the period just after 9/11 during Blair’s second term as prime minister.

On Sunday, Alan Johnson, the Labour former home secretary, told the Marr show that the last government had looked into the claims and had not found any evidence of British involvement.

“When I was home secretary, when David Miliband was foreign secretary, we didn’t just sit there and say: ‘We’ll take what the agencies tell us’,” he said.

“We made very thorough investigations. We reported to the intelligence and security committee under its previous chair, Kim Howells, on this. We could find no evidence of British agents being involved.”

He also defended the decision of the UK government to request redactions to the report, saying he agreed with Theresa May, the home secretary.

“What she would have done there – and it’s right incidentally that the intelligence and security committee see what was redacted so they can be assured that this was to protect sources – it was to protect British agents in the field,” he said.

“And it’s inconceivable that an American Senate committee actually being very, very open about what America was doing would somehow agree to Britain redacting the same information … So I am absolutely convinced that what was redacted was what the Home Office said they wanted redacting.”